The board / number theory / #280
Erdős Problem #280
DISPROVED LEANdatabase updated 2026-04-18
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The integer `m` is covered by one of the first `k` chosen congruence classes.
The number of integers below `n k` not covered by the first `k` congruence classes.
Let \(n_1<n_2<\cdots \) be an infinite sequence of integers with associated \(a_k\pmod{n_k}\), such that for some \(\epsilon>0\) we have \(n_k>(1+\epsilon)k\log k\) for all \(k\). Then \[ \#\{ m<n_k : m\not\equiv a_i\pmod{n_i} \textrm{ for }1\leq i\leq k\}\neq o(k). \] Cambie observed that this is false.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/280.Prizenone
Topicsnumber theory, covering systems
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/280
Attempts
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